论文标题
普遍的Lipschitz正则化等于分布鲁棒性
Generalised Lipschitz Regularisation Equals Distributional Robustness
论文作者
论文摘要
对抗性示例的问题强调了对正则化理论的必要性，该理论足以适用于外来功能类别，例如通用近似值。作为回应，我们在分布鲁棒性和正则化之间的关系中给出了非常普遍的平等结果，这是通过运输成本不确定性集定义的。该理论使我们能够（紧密地）以非常温和的假设来证明Lipschitz登记模型的鲁棒性特性。作为理论应用，我们显示了一个新的结果，该结果阐明了对抗性学习和分布鲁棒性之间的联系。然后，我们为如何实现内核分类器的Lipschitz正则化提供了新的结果，这些结果已通过实验证明。
The problem of adversarial examples has highlighted the need for a theory of regularisation that is general enough to apply to exotic function classes, such as universal approximators. In response, we give a very general equality result regarding the relationship between distributional robustness and regularisation, as defined with a transportation cost uncertainty set. The theory allows us to (tightly) certify the robustness properties of a Lipschitz-regularised model with very mild assumptions. As a theoretical application we show a new result explicating the connection between adversarial learning and distributional robustness. We then give new results for how to achieve Lipschitz regularisation of kernel classifiers, which are demonstrated experimentally.
